A226654 Decimal expansion of the 1st Lebesgue constant L1.

1, 4, 3, 5, 9, 9, 1, 1, 2, 4, 1, 7, 6, 9, 1, 7, 4, 3, 2, 3, 5, 5, 9, 8, 6, 3, 2, 9, 9, 5, 9, 2, 7, 2, 2, 1, 6, 1, 2, 8, 1, 0, 6, 2, 9, 4, 0, 6, 6, 6, 1, 4, 6, 3, 8, 9, 3, 2, 0, 6, 5, 3, 7, 3, 9, 1, 5, 3, 9, 3, 9, 4, 0, 2, 7, 1, 8, 7, 2, 9, 2, 3, 0, 1, 4, 0, 9, 3, 3, 9, 0, 9, 7, 9, 6, 7, 5, 1, 1, 1, 7, 4, 8, 7

Offset

1,2

Comments

Named after the French mathematician Henri Léon Lebesgue (1875-1941). - Amiram Eldar, Jun 19 2021

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 251.

Links

Table of n, a(n) for n=1..104.

Henri Lebesgue, Sur la représentation trigonométrique approchée des fonctions satisfaisant à une condition de Lipschitz, Bulletin de la Société Mathématique de France, Vol. 38 (1910), pp. 184-210.

Eric Weisstein's MathWorld, Lebesgue constants.

Formula

Equals (1/Pi) * Integral_{t=0..Pi} abs(sin(3*t/2))/sin(t/2) dt.

Equals 1/3 + 2*sqrt(3)/Pi.

Example

1.43599112417691743235598632995927221612810629406661463893206537391539394...

Mathematica

RealDigits[1/3 + 2*Sqrt[3]/Pi, 10, 100][[1]]

Crossrefs

Cf. A226655 (L2), A226656 (L3).

Sequence in context: A227684 A200636 A229938 * A124451 A277261 A140391

Adjacent sequences: A226651 A226652 A226653 * A226655 A226656 A226657

Keyword

cons,nonn

Author

Jean-François Alcover, Jun 14 2013

Status

approved